The present invention relates generally to reproducing images in three dimensions and more particularly to synthesizing holograms digitally and reproducing images in three dimensions from those holograms.
Several techniques for reproducing images in three dimensions are known in the art.
Some systems, referred to as xe2x80x9cstereoscopicxe2x80x9d, produce two offset images of the same scene, each of which is viewed by a respective eye of an observer. Depth of field and volume are then reconstructed by the brain of the observer. The majority of such systems necessitate the wearing of bulky accessories such as glasses or helmets to separate and differentiate the images sent to each eye. Also, they present only one angle of binocular vision of the scene to be represented.
Another technique, referred to as xe2x80x9cautostereoscopicxe2x80x9d, consists in one particular instance in taking a photograph of a scene through a plane array of sufficiently small lenses, so as to associate each lens with a respective point of view of the photographed scene. The photograph obtained in this way gives the illusion of relief, but produces a limited effect of depth. This method does not conform to the natural accommodation of the eye, and in the current state of the art, reproducing three-dimensional images in real-time by this method is difficult.
Holography is the most faithful method of reproducing three-dimensional images because it reproduces the optical field generated by the scene. In particular, this method conforms perfectly to the accommodation of the eye. Analogue holography consists in projecting a coherent light wave emitted by a laser onto an object, picking up from this wave a light wave diffused by the object, and causing the diffused light wave to interfere with a reference wave consisting of another part of the beam emitted by the laser to produce an interference field. The interference field is recorded in a photosensitive medium such as a photographic plate. An image of the original scene in three dimensions can then be observed by illuminating the photographic plate with a coherent wave. This purely analogue method provides excellent reproduction quality but cannot reproduce three-dimensional images in real time.
Digital holographic methods of producing three-dimensional images in real time are known in the art. U.S. Pat. No. 5,668,648 describes a computer-assisted holographic apparatus capable of digitally synthesizing the hologram of a virtual object and reproducing an image from that hologram. The virtual object is sampled into sampling points which are considered as individual spherical light sources. Respective diffraction fields are calculated for the sampling points and are then superposed. An interpolation technique is used to improve the resolution of the resulting diffraction field. An interference field (hologram) is then generated as a function of the resulting diffraction field and data representing a reference wave and is physically reproduced by a spatial light modulator.
Synthesizing holograms digitally by the above method necessitates long and complex calculations, in particular to determine a diffraction field associated with each sampling point of the object and to interpolate the resulting diffraction field.
The present invention aims to provide a holographic method that is capable of efficient spatial reproduction of three-dimensional images in real time.
To this end, there is provided a method of reproducing at least a portion of a three-dimensional image, said three-dimensional image being represented by digital data and defined in a three-dimensional geometrical space, which method is characterized in that it comprises the following steps:
calculating a set of two-dimensional images obtained by determining, in the three-dimensional geometrical space, respective intersections between the three-dimensional image and a plurality of section planes,
calculating a hologram for each of the two-dimensional images, and
successively reproducing the holograms of the two-dimensional images on a spatial light modulator illuminated by a light source.
The present invention finds a particularly suitable application in the medical field. The three-dimensional image reproduced by the above method is transparent, enabling the interior of organs to be visualized. Other applications can be envisaged, however, especially in the fields of consumer imaging (TV, cinema), and telecommunications.
The light source is typically a spatially coherent monochromatic light source emitting at a predetermined wavelength and the holograms of the two-dimensional images are calculated for said wavelength.
The spatial light modulator is advantageously a liquid crystal screen having a pixel pitch of less than 10 xcexcm and preferably close to 1 xcexcm in at least two different directions. By xe2x80x9cpixel pitchxe2x80x9d is meant the period of reproduction of pixels in a given direction, which, for each pixel, corresponds to the sum of the size of the pixel in the given direction plus the distance separating that pixel from an adjacent pixel in the same direction. The distance between two pixels is chosen to be as small as possible and preferably substantially zero. The above-mentioned two different directions respectively correspond to rows and columns of pixels on the liquid crystal screen.
In order to reproduce the three-dimensional image faithfully, the section planes are preferably parallel.
Said step of successively reproducing the holograms consists in repetitively reproducing on the spatial light modulator a sequence consisting of the holograms. The sequence advantageously has a duration not exceeding 50 ms, so that an observer can effortlessly view the image in three dimensions by mental fusion.
In the invention, in said step of calculating a hologram for each of the two-dimensional images, the holograms of the two-dimensional images are calculated in a predetermined plane situated at a finite distance from the plurality of section planes and preferably parallel thereto. This conforms perfectly to the geometry and the proportions of the three-dimensional image and prevents it being reproduced in a deformed (xe2x80x9ccrushedxe2x80x9d) fashion.
The two-dimensional images are typically defined by respective real functions and said step of calculating a hologram for each of the two-dimensional images comprises the following steps for a given two-dimensional image:
transforming the given two-dimensional image defined by the corresponding real function into a complex two-dimensional image defined by a complex function,
oversampling the complex image,
simulating the production of a diffracted image resulting from-the diffraction of a light wave by the oversampled complex image,
adding a complex field representing a reference light wave to the resulting diffracted image, and
coding values taken by the amplitude of the sum of said complex field and the resulting diffracted image to produce the hologram associated with said given two-dimensional image.
Said simulation step advantageously consists in calculating a convolution product, associated with the oversampled complex image, of two components, by applying the transform which is the inverse of a predetermined complex transform to the product of the respective complex transforms of said two components. The predetermined complex transform is, for example, one of the following complex transforms: Fourier transform, Walsh transform, Hankel transform, orthogonal polynomial transform, Hadamar transform, Karhunen-Loeve transform, multiresolution discrete wavelet transform, adaptive wavelet transform, and a transform resulting from composing two or more of the above transforms.
The three-dimensional image can be a color image. In this case, the method of the invention further comprises a step of decomposing each of the two-dimensional images into red, green, and blue (RGB) two-dimensional images respectively, said step of calculating a hologram for each of the two-dimensional images consisting, for a given red, green, or blue two-dimensional image, in producing a hologram for a wavelength corresponding to the color of the given two-dimensional image, and said step of successively reproducing the holograms consisting in reproducing the holograms of the two-dimensional images successively on the spatial light modulator while the latter is illuminated in turn by coherent red, green, and blue light waves respectively as a function of the color for which the hologram reproduced on the spatial light modulator was calculated.
The invention also provides a method of reproducing, in three dimensions, a video film consisting of a sequence of three-dimensional images represented by digital data, characterized in that the method consists in applying the above-defined method to each three-dimensional image of said sequence so that, for each three-dimensional image, holograms corresponding to that image are reproduced successively on a spatial light modulator during a predetermined image cycle.
The invention further provides an apparatus for reproducing at least a portion of a three-dimensional image, said three-dimensional image being represented by digital data and defined in a three-dimensional geometrical space, which apparatus is characterized in that it comprises:
means for storing the three-dimensional image,
means for calculating a set of two-dimensional images obtained by determining in the three-dimensional geometrical space respective intersections between the three-dimensional image and a plurality of section planes,
means for calculating a hologram for each of the two-dimensional images,
a spatial light modulator for successively reproducing the holograms of the two-dimensional images, and
a light source for illuminating the spatial light modulator during the reproduction thereby of said holograms.
Said means for calculating a hologram for each of the two-dimensional images typically comprise means for calculating the holograms of the two-dimensional images in a predetermined plane situated at a finite distance from the plurality of section planes and preferably parallel thereto.
To be more precise, said means for calculating a hologram for each of the two-dimensional images comprise:
means for transforming a given two-dimensional image defined by the corresponding real function into a complex two-dimensional image defined by a complex function,
means for oversampling the complex image,
means for simulating the production of a diffracted image resulting from the diffraction of a light wave by the oversampled complex image,
means for adding a complex field representing a reference light wave to the resulting diffracted image, and
means for coding values taken by the amplitude of the sum of said complex field and the resulting diffracted image to produce the hologram associated with said given two-dimensional image.
Said means for simulating the production of a diffracted image can comprise means for calculating a convolution product, associated with the oversampled complex image, of two components, by applying the transform which is the inverse of a predetermined complex transform to the product of the respective complex transforms of said two components.
When the three-dimensional image is a color image, the apparatus of the invention further comprises means for decomposing each of the two-dimensional images into red, green, and blue (RGB) two-dimensional images respectively, said means for calculating a hologram for each of the two-dimensional images then comprising means for producing, for a given red, green, or blue two-dimensional image, a hologram for a wavelength corresponding to the color of the given two-dimensional image, and the spatial light modulator reproducing the holograms of the two-dimensional images successively while it is illuminated in turn by light sources emitting coherent red, green, and blue light waves respectively as a function of the color for which the hologram reproduced on the spatial light modulator was calculated.
The present invention also provides an apparatus for reproducing, in three dimensions, a video film consisting of a sequence of three-dimensional images represented by digital data, characterized in that it comprises means for applying each three-dimensional image of said sequence to the above-defined apparatus so that, for each three-dimensional image, holograms corresponding to that image are reproduced on a spatial light modulator during a predetermined image cycle.